Production of $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ from ${\mathrm{\Xi }}_b$ decay

In the present work, we investigate the production of the newly observed $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ state in ${\mathrm{\Xi }}_b^{-}$ decay, where the $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ is assigned as a ${\mathrm{\Xi }}_c\bar{D}$ molecular state. By using an effective Lagrangian approach, we evaluate the branching fractions of ${\mathrm{\Xi }}_b^{-}\to P_{\psi s}^{\mathrm{\Lambda }}(4338)K^{-}$ via the triangle loop mechanism. The branching fractions of ${\mathrm{\Xi }}_b^{-}\to P_{\psi s}^{\mathrm{\Lambda }}(4338)K^{-}$ are in the order of ${10}^{-4}$; the result is compared with our previous work of ${\mathrm{\Xi }}_b^{-}\to P_{\psi s}^{\mathrm{\Lambda }}(4459)K^{-}$. We also predict the ratio of $P_{\psi s}^{\mathrm{\Lambda }}(4459)$ and $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ productions in the decay ${\mathrm{\Xi }}_b^{-}\to P_{\psi s}^{\mathrm{\Lambda }}{K}^{-}\to J\mathrm{/}\psi \mathrm{\Lambda }{K}^{-}$. The predicted branching fractions and their ratios could be tested experimentally, which may be helpful for understanding the molecular picture of $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ as well as other hidden-charm pentaquark states with strangeness. Moreover, the experimental potential of observing $P_{\psi s}^{\mathrm{\Lambda }}(4338)$ in the ${\mathrm{\Xi }}_b^{-}\to K^{-}J\mathrm{/}\psi \mathrm{\Lambda }$ is discussed.